In an apparatus for constructing a high-rising, poured concrete wall or shape, pairs of spaced-apart, upright supports are preliminarily mounted on a foundation and then detachably attached to both sides of at least a partially hardened level of concrete wall and at intervals along the length of the wall for repeated, upward, step-wise use as the wall is being formed; a plurality of carriages are mounted on adjacent supports along both sides of the wall for continuous upward movement as the wall is being cast, and adjustable concrete shaping assemblies are mounted on the carriages each assembly opposing a similar assembly to define a continuous mold into which new concrete is poured on top of previously poured concrete to form the wall. The method of constructing such a wall, by repeated, step-wise use of upright supports attached to lower sections of partially hardened concrete, and said supporting mounting a plurality of movable carriages, each holding a concrete shaping assembly, and pouring concrete into the assemblies along the entire length of the wall as the assemblies move continuously upwardly in unison on the supports.